MinT - Information on Result #2639065

Information on Result #2639065

Linear OOA(4²⁵⁹, 106, F₄, 3, 181) (dual of [(106, 3), 59, 182]-NRT-code), using strength reduction based on linear OOA(4²⁵⁹, 106, F₄, 3, 182) (dual of [(106, 3), 59, 183]-NRT-code), using

constructionÂ X applied to AG(3;F,126P) âŠ‚ AG(3;F,131P) [i] based on
1. linear OOA(4²⁵⁵, 103, F₄, 3, 182) (dual of [(103, 3), 54, 183]-NRT-code), using algebraic-geometric NRT-code AG(3;F,126P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
  - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4²⁵⁰, 103, F₄, 3, 177) (dual of [(103, 3), 59, 178]-NRT-code), using algebraic-geometric NRT-code AG(3;F,131P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104 (see above)
3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;8,4) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.